LaPSO {LHD}

Particle Swarm Optimization for LHD

Description

LaPSO returns a n by k LHD matrix generated by particle swarm optimization algorithm (PSO)

Usage

LaPSO(
  n,
  k,
  m = 10,
  N = 10,
  SameNumP = 0,
  SameNumG = n/4,
  p0 = 1/(k - 1),
  OC = "phi_p",
  p = 15,
  q = 1,
  maxtime = 5
)

Arguments

n

A positive integer, which stands for the number of rows (or run size).

k

A positive integer, which stands for the number of columns (or factor size).

m

A positive integer, which stands for the number of particles. The default is set to be 10. A large value of m will result a high CPU time, and it is recommended to be no greater than 100.

N

A positive integer, which stands for the number of iterations. The default is set to be 10. A large value of N will result a high CPU time, and it is recommended to be no greater than 500.

SameNumP

A non-negative integer, which stands for how many elements in current column of current particle LHD should be the same as corresponding Personal Best. SameNumP=0, 1, 2, ..., n, and 0 means to skip the "exchange". The default is set to be 0.

SameNumG

A non-negative integer, which stands for how many elements in current column of current particle LHD should be the same as corresponding Global Best. SameNumP=0, 1, 2, ..., n, and 0 means to skip the "exchange". The default is set to be n/4. SameNumP and SameNumG cannot be 0 at the same time.

p0

A probability of exchanging two randomly selected elements in current column of current particle LHD. The default is set to be 1/(k - 1).

OC

An optimality criterion. The default setting is "phi_p", and it could be one of the following: "phi_p", "AvgAbsCor", "MaxAbsCor", "MaxProCriterion".

p

A positive integer, which is the parameter in the phi_p formula, and p is prefered to be large. The default is set to be 15.

q

The default is set to be 1, and it could be either 1 or 2. If q is 1, dij is the Manhattan (rectangular) distance. If q is 2, dij is the Euclidean distance.

maxtime

A positive number, which indicates the expected maximum CPU time given by user, and it is measured by minutes. For example, maxtime=3.5 indicates the CPU time will be no greater than three and half minutes. The default is set to be 5.

Value

If all inputs are logical, then the output will be a n by k LHD. Here are some general suggestions about the parameters:

• SameNumP is approximately n/2 when SameNumG is 0.

• SameNumG is approximately n/4 when SameNumP is 0.

• p0 * (k - 1) = 1 to 2 is often sufficient. So p0 = 1/(k - 1) to 2/(k - 1).

References

Chen, R.-B., Hsieh, D.-N., Hung, Y., and Wang, W. (2013) Optimizing Latin hypercube designs by particle swarm. Stat. Comput., 23, 663-676.

Examples

#generate a 5 by 3 maximin distance LHD with the default setting
try=LaPSO(n=5,k=3)
try
phi_p(try)   #calculate the phi_p of "try".

#Another example
#generate a 8 by 4 nearly orthogonal LHD
try2=LaPSO(n=8,k=4,OC="AvgAbsCor")
try2
AvgAbsCor(try2)  #calculate the average absolute correlation.